Deformation and breakup of viscoelastic droplets in confined shear flow

Understanding Deformation and Breakup Tendency of Shear-Thinning Viscoelastic Drops in Constricted Microchannels

The study of drop deformation in response to various stresses has long piqued the interest of several academics. The deformation behavior of cells, drug carriers, and even drug particles moving via microcapillaries inside the human body can be modeled using a viscoelastic drop model. A drop breakup study can also provide better design guidance for nanocarriers that can deliver on-demand burst drug releases at specific cancer sites. Thus, we attempted to investigate the deformation and breakup of a shear-thinning finitely extensible nonlinear elastic-peterlin (FENE-P) drop moving through the constricted microchannel. The computational simulation suggested that drop deformation and breakup can be manipulated by varying of parameters like channel confinement, Deborah number, solvent viscosity ratio, viscosity ratio, and capillary number. We attempted to find the critical capillary number for initiation of drop breakup. Observations from present study will give valuable insights into deformation and breakup patterns of drug carriers inside constricted microcapillaries. The simulations of the two-phase viscoelastic drop─Newtonian matrix system were performed on an open-source solver, Basilisk.

Cross-stream migration of a Brownian droplet in a polymer solution under Poiseuille flow

The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial effects at the studied flow conditions, in agreement with theoretical predictions and recent simulations. However, the droplet focused onto the channel centerline when polymer chains were added to the solvent. Focusing was typically enhanced for longer polymers and higher polymer concentrations with a nontrivial flow-rate dependence due to droplet and polymer deformability. Brownian motion caused the droplet position to fluctuate with a distribution that primarily depended on the balance between inertial lift forces pushing the droplet outward and elastic forces from the polymers driving it inward. The droplet shape was controlled by the local shear rate, and so its average shape depended on the droplet distribution.

Electrokinetic droplet transport from electroosmosis to electrophoresis

Droplet transport in microfluidic channels by electrically induced flows often entails the simultaneous presence of electroosmosis and electrophoresis. Here we make use of coupled lattice-Boltzmann/molecular dynamics simulations to compute the mobility of a droplet in a microchannel under the effect of an external electric field. By varying the droplet solvation free energy of the counterions released at the channel walls, we observe the continuous transition between the electroosmotic and electrophoretic regime. We show that it is possible to describe the mobility of a droplet in a unified, consistent way, by combining the theoretical description of the electroosmotic flow with, in this case, the Hückel limit of electrophoresis, modified in order to take into account the Hadamard-Rybczynski droplet drag.

Modified two-step emulsion solvent evaporation technique for fabricating biodegradable rod-shaped particles in the submicron size range

HYPOTHESIS

Though the emulsion solvent evaporation (ESE) technique has been previously modified to produce rod-shaped particles, it cannot generate small-sized rods for drug delivery applications due to the inherent coupling and contradicting requirements for the formation versus stretching of droplets. The separation of the droplet formation from the stretching step should enable the creation of submicron droplets that are then stretched in the second stage by manipulation of the system viscosity along with the surface-active molecule and oil-phase solvent.

EXPERIMENTS

A two-step ESE protocol is evaluated where oil droplets are formed at low viscosity followed by a step increase in the aqueous phase viscosity to stretch droplets. Different surface-active molecules and oil phase solvents were evaluated to optimize the yield of biodegradable PLGA rods. Rods were assessed for drug loading via an imaging agent and vascular-targeted delivery application via blood flow adhesion assays.

FINDINGS

The two-step ESE method generated PLGA rods with major and minor axis down to 3.2 µm and 700 nm, respectively. Chloroform and sodium metaphosphate was the optimal solvent and surface-active molecule, respectively, for submicron rod fabrication. Rods demonstrated faster release of Nile Red compared to spheres and successfully targeted an inflamed endothelium under shear flow in vitro and in vivo.

Water Droplet Dynamics on a Hydrophobic Surface in Relation to the Self-Cleaning of Environmental Dust

The dynamic motion of a water droplet on an inclined hydrophobic surface is analyzed with and without environmental dust particles on the surface. Solution crystallization of a polycarbonate surface is carried out to generate a hydrophobic surface with hierarchical texture composed of micro/nanosize spheroids and fibrils. Functionalized nanosize silica particles are deposited on the textured surface to reduce contact angle hysteresis. Environmental dust particles are collected and characterized using analytical tools prior to the experiments. The droplet motion on the hydrophobic surface is assessed using high-speed camera data, and then, the motion characteristics are compared with the corresponding analytical results. The influence of dust particles on the water droplet motion and the amount of dust particles picked up from the hydrophobic surface by the moving droplet is evaluated experimentally. A 40 μL droplet was observed to roll on the hydrophobic surface with and without dust particles, and the droplet slip velocity was lower than the rotational velocity. The rolling droplet removes almost all dust particles from the surface, and the mechanism for the removal of dust particles from the surface was determined to be water cloaking of the dust particles.

Lattice Boltzmann simulations of droplet dynamics in time-dependent flows

We study the deformation and dynamics of droplets in time-dependent flows using 3D numerical simulations of two immiscible fluids based on the lattice Boltzmann model (LBM). Analytical models are available in the literature, which assume the droplet shape to be an ellipsoid at all times (P.L. Maffettone, M. Minale, J. Non-Newton. Fluid Mech 78, 227 (1998); M. Minale, Rheol. Acta 47, 667 (2008)). Beyond the practical importance of using a mesoscale simulation to assess "ab initio" the robustness and limitations of such theoretical models, our simulations are also key to discuss --in controlled situations-- some relevant phenomenology related to the interplay between the flow time scales and the droplet time scales regarding the "transparency" transition for high enough shear frequencies for an external oscillating flow. This work may be regarded as a step forward to discuss extensions towards a novel DNS approach, describing the mesoscale physics of small droplets subjected to a generic hydrodynamical strain field, possibly mimicking the effect of a realistic turbulent flow on dilute droplet suspensions.

Morphology Evolution of Polymer Blends under Intense Shear During High Speed Thin-Wall Injection Molding

The morphology evolution under shear during different processing is indeed an important issue regarding the phase morphology control as well as final physical properties of immiscible polymer blends. High-speed thin wall injection molding (HSTWIM) has recently been demonstrated as an effective method to prepare alternating multilayered structure. To understand the formation mechanism better and explore possible phase morphology for different blends under HSTWIM, the relationship between the morphology evolution of polymer blends based on polypropylene (PP) under HSTWIM and some intrinsic properties of polymer blends, including viscosity ratio, interfacial tension, and melt elasticity, is systematically investigated in this study. Blends based on PP containing polyethylene (PE), ethylene vinyl alcohol copolymer (EVOH), and polylactic acid (PLA) are used as examples. Compatibilizer has also been added into respective blends to alter their interfacial interaction. It is demonstrated that dispersed phase can be deformed into a layered-like structure if interfacial tension, viscosity ratio, and melt elasticity are relatively small. While some of these values are relatively large, these dispersed droplets are not easily deformed under HSTWIM, forming ellipsoidal or fiber-like structure. The addition of a moderate amount of compatibilizer into these blends is shown to be able to reduce interfacial tension and the size of dispersed phase, thus, allowing more deformation on the dispersed phase. Such a study could provide some guidelines on phase morphology control of immiscible polymer blends under shear during various processing methods.

Stretching of viscoelastic drops in steady sliding

The sliding of non-Newtonian drops down planar surfaces results in a complex, entangled balance between interfacial forces and non-linear viscous dissipation, which has been scarcely inspected. In particular, a detailed understanding of the role played by the polymer flexibility and the resulting elasticity of the polymer solution is still lacking. To this aim, we have considered polyacrylamide (PAA) solutions of different molecular weights, suspended either in water or in glycerol/water mixtures. In contrast to drops of stiff polymers, drops of flexible polymers exhibit a remarkable elongation in steady sliding. This difference is most likely attributed to variation of viscous bending as a consequence of variation of shear thinning. Moreover, an "optimal elasticity" of the polymer seems to be required for this drop elongation to be visible. We have complemented experimental results with numerical simulations of a viscoelastic FENE-P drop. This has been a decisive step to unraveling how a change of the elastic parameters (e.g. polymer relaxation time, maximum extensibility) affects the dimensionless sliding velocity.

Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations

We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)CMPHAY0010-361610.1007/BF01212349]. By taking an L^{∞} norm of the energy of the full binary system, designated as E_{∞}, we have shown that ∫_{0}^{t}E_{∞}(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 128^{3} to 512^{3} collocation points and over the duration of our DNSs confirm that E_{∞} remains bounded as far as our computations allow.

Effects of viscoelasticity on droplet dynamics and break-up in microfluidic T-Junctions: a lattice Boltzmann study

The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number (Ca), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to Ca ≈ 3×10(-2). A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of Ca which is broad enough to characterize all the three characteristic mechanisms of break-up in the confined T-junction, i.e. squeezing, dripping and jetting regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time τP and the finite extensibility parameter L2, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with Droplet Viscoelasticity (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with Matrix Viscoelasticity (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios Q ≈ O(1) of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.

A lattice Boltzmann study of the effects of viscoelasticity on droplet formation in microfluidic cross-junctions

Based on mesoscale lattice Boltzmann (LB) numerical simulations, we investigate the effects of viscoelasticity on the break-up of liquid threads in microfluidic cross-junctions, where droplets are formed by focusing a liquid thread of a dispersed (d) phase into another co-flowing continuous (c) immiscible phase. Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) to droplet formation downstream of the cross-junction (DC) (Liu and Zhang, Phys. Fluids. 23, 082101 (2011)). We will analyze cases with Droplet Viscoelasticity (DV), where viscoelastic properties are confined in the dispersed phase, as well as cases with Matrix Viscoelasticity (MV), where viscoelastic properties are confined in the continuous phase. Moderate flow-rate ratios Q≈O(1) of the two phases are considered in the present study. Overall, we find that the effects are more pronounced with MV, where viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is attributed to an increase of the polymer feedback stress forming in the corner flows, where the side channels of the device meet the main channel. Quantitative predictions on the break-up point of the threads are provided as a function of the Deborah number, i.e., the dimensionless number measuring the importance of viscoelasticity with respect to Capillary forces.

Deformation of double emulsions under conditions of flow cytometry hydrodynamic focusing

Water-in-oil-in-water (w/o/w) microfluidics double emulsions offer a new route to compartmentalise reagents into isolated aqueous microenvironments while maintaining an aqueous carrier fluid phase; this enables compatibility with commercial flow cytometry systems such as fluorescence-activated cell sorting (FACS). Double emulsion (inner core) deformation under hydrodynamic focusing conditions that mimic the environment double emulsions experience in flow cytometry applications is of particular importance for droplet stability and cell viability. This paper reports on an experimental study of the dynamic deformation of aqueous cores of w/o/w double emulsions under hydrodynamic focusing, with the sheath flow directed at 45° to the sample flow. A number of factors affecting the inner core deformation and recovery were examined. Deformation was found to depend significantly on the core or shell viscosity, the droplet-to-sheath flow velocity ratio, and core and shell sizes. Core deformation was found to depend more on the type of surfactant rather concentration with high molecular weight surfactant exhibiting a negligible effect on deformation whereas low molecular weight surfactant enhancing deformation at low concentrations due to their lateral mobility at the interface.

Sliding droplets of Xanthan solutions: A joint experimental and numerical study

We have investigated the sliding of droplets made of solutions of Xanthan, a stiff rodlike polysaccharide exhibiting a non-Newtonian behavior, notably characterized by a shear thinning viscosity accompanied by the emergence of normal stress difference as the polymer concentration is increased. These experimental results are quantitatively compared with those of Newtonian fluids (water). The impact of the non-Newtonian behavior on the sliding process was shown through the relation between the average dimensionless velocity (i.e. the capillary number) and the dimensionless volume forces (i.e. the Bond number). To this aim, it is needed to define operative strategies to compute the capillary number for the shear thinning fluids and compare with the corresponding Newtonian case. The resulting capillary number for the Xanthan solutions scales linearly with the Bond number at small inclinations, as well known for Newtonian fluids, while it shows a plateau as the Bond number is increased. Experimental data were complemented with lattice Boltzmann numerical simulations of sliding droplets, aimed to disentangle the specific contribution of shear thinning and elastic effects on the sliding behavior. In particular the deviation from the linear (Newtonian) trend is more likely attributed to the emergence of normal stresses inside the non-Newtonian droplet.